Writing Homework Help

pick one math topic on the file and write about it 2 pages

Writing Assignments 1

Imagine that you’re a consultant for a city that is considering changing its election rules. Currently, as is usual in elections, each voter votes for one candidate from the list of those running. A majority vote is required for election. If no candidate has a majority, there is a run off election between the two candidates with the most votes. As an alternative to a runoff election, the city is considering adopting the method of plurality-with-elimination (instant runoff voting) and the city council has asked you for guidance.

Prepare a report for your city council on this matter. Include in your report the following items.

• A clear explanation of what plurality with elimination is and how it works;
• A worked-out solution to problem? (show all steps), presented as an example illustrating your explanation;
• A discussion of the pros and cons of plurality-with-elimination versus Borda Method elections—include any economic, social, or political considerations you can think of.

Conclude your report with a recommendation either for or against plurality-with-elimination; give reasons for your recommendation.

Remember that your city council members are not as well versed as you are in the mathematical aspects of elections. Part of your job is to educate them.

Your report should be typewritten (word processed) if possible, no handwritten report. There is no minimum or maximum page length. Write a report you think is effective, no matter how long or short it is. Show the appropriate steps and worksheet.

Writing Assignments 2

Your city is thinking of buying computer software that will find the most efficient routes for various processes such as snow plowing and parking meter enforcement. The software uses techniques like the ones in Chapter 5 to find these routes. Because of the cost involved in buying the software, your city council is opposed to the idea. The problem is that some on the council don’t understand what the software will do, and don’t see the need of having a computer determine routes.

Write a letter to your city council in favor of buying the software. Include:

• A clear explanation of what the software will do;
• A worked-out solution to Exercise 53 on p. 168 (show all steps), presented as an example illustrating your explanation;
• An explanation of why a computer program is needed to solve similar problems in your real-life city (as opposed to doing it by hand);
• A discussion of how the computer program will benefit your city.

Page 168 Exercise #53

A security guard must patrol on foot the streets of the Green Hills subdivision shown in Figure 5.39. The security guard wants to start and end his walk at the corner labeled A, and he needs to cover each block of the subdivision at least once. Find an optimal route for the security guard. Describe the route by labeling the edges 1, 2, 3, and so on in the order in which they are traveled. (Hint: you should do exercise 21 first)

Page 165 Exercise #21

A night watchman must walk the streets of the Green Hills subdivision shown in Figure 5.39. The night watchman needs to walk only once along each block. Draw a graph that models this street routing problem.

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Remember that your city council members are not as well versed as you are in the mathematical aspects of this issue. Part of your job is to educate them.

Your report should be typewritten (word processed) if possible, although I will accept a handwritten report if it is neat and easy to read. There is no minimum or maximum page length. Write a report you think is effective, no matter how long or short it is.

Writing Assignments 3 _- Find the Banzhaf Power and Shapley-Shubik Power [10: 7, 4, 2, 1]

• Find the Banzhaf Power [10: 7, 4, 2, 1]
• Shapley-Shubik Power [10: 7, 4, 2, 1]
• Is there a Dictator?
• Who has Veto Power?

Writing Assignments 4 – Hamilton Circuits in KN

• If N = 36

Listed below are four key properties of KN:

• The degree of every vertex in KN is
• The number of edges in KN is
• The number of Hamilton paths in KN is
• The number of Hamilton circuits in KN